Regenerative adsorption process and multi-reactor regenerative adsorption chiller

ABSTRACT

A regenerative adsorption process and a multi-reactor regenerative adsorption chiller assembly including a condenser adapted to receive a coolant from a source; an evaporator connected to the condenser to provide a refrigerant circuit; a plurality of reactors, each being able to operate in adsorption and desorption modes and having a coolant inlet to directly or indirectly receive coolant when operating in adsorption mode before, after or simultaneous with the condenser, and a waste heat inlet for directly or indirectly receiving waste heat from a waste heat source when operating in desorption mode; and control means for controlling said plurality of reactors such that each reactor alternately operates in adsorption and desorption modes for substantially identical time intervals, and such that each reactor has an equal chance of being the first reactor to receive the coolant when operating in adsorption mode, and the waste heat from the waste heat source when operating in desorption mode.

FIELD OF THE INVENTION

[0001] This invention relates to a regenerative adsorption process andan adsorption chiller designed for utilising waste heat typically havinga temperature of below about 150° C. for useful cooling.

BACKGROUND OF THE INVENTION

[0002] Two-reactor adsorption chillers have already been successfullycommercialised in Japan [1,2]. By making use of a silica gel-waterworking pair, such chillers have managed to economically harness thepotential of low-grade waste heat for useful cooling before it isdischarged into the environment. Insofar as adsorption chillers areconcerned, some methods have been devised to improve the conversionefficiency of the potential waste heat to useful cooling. For example,schemes have been proposed where such waste heat is used serially in astring of adsorption chillers before it is finally discharged. Asanother example, a scheme has previously been proposed where thedesorption temperature is significantly reduced by means of multi-stagethermal compression of the refrigerant vapour [3]. This enables wasteheat to be further utilized before it is finally purged to theenvironment. From the trend of development of the prior art, it would bedesirable to further improve the conversion efficiency so that maximumcooling capacity can be derived from a given hardware investment, wasteheat and coolant flow rate.

[0003] Of equal importance is the need for a stable chilled water outlettemperature. Based on experimental measurement on a commerciallyavailable 10 kW two-reactor adsorption chiller, under a typical dynamicsteady state operation, the chilled water outlet temperature generallyfluctuates by ±1.5° C. [4]. While such fluctuation may be acceptable forsensible cooling and rough process cooling requirements, it begins topose a problem in dehumidification, and other stringent coolingapplications. In the latter field of usage, vapour compression orabsorption cooling devices have been employed downstream to attenuatethe temperature oscillation. It would therefore be desirable to providea smoother chilled water outlet temperature so that downstreamtemperature smoothening devices could be downsized or even eliminated.

[0004] Sato et al. [5-6] have proposed a multi-reactor strategyinvolving cooling the adsorber with refrigerant emanating from one ormore evaporators. It may be desirable and more practical to have theevaporator devoted to cooling the chilled water, with the evaporatedrefrigerant being superheated at the adsorbers. Master-and-slaveconfiguration is commonly found in these references for the arrangementof the reactors. Such master-and-slave configurations for the string ofreactors may represent an under-utilization of downstream reactors. Itwould therefore be attractive to eliminate such rigid configuration.

[0005] Many other designs [7-14] employ re-circulating fluid to boostthe chiller's coefficient of performance. These arrangements aredesigned for use with a high temperature heat source, which is usuallyeconomically valuable; they are done at the expense of a lower firingtemperature for the desorber and a higher cooling temperature for theadsorber. In the case of low temperature (typically 150° C. or below)waste heat application, such a strategy may not be feasible. In thiscase, the objective would then be to maximise the cooling throughput ofthe chiller.

[0006] The present invention advantageously improves the recoveryefficiency of waste heat to useful cooling. Recognizing that coolingwater for the adsorber and condenser is a scarce resource, the inventionaspires to achieve maximum cooling capacity for a given flow rate ofwaste heat and cooling stream. This advantageously also ensures maximumconversion efficiency of waste heat to useful cooling and reduces pipingmaterial for a given cooling capacity.

[0007] Advantageously, the invention also makes it possible to downsizeor even eliminate the need for downstream temperature smootheningdevices by providing a more stable chilled water outlet temperature.

[0008] Further, the invention advantageously reduces the risk of iceformation by providing for a sequential start-up of the reactor orreactors when the chiller is activated.

SUMMARY OF THE INVENTION

[0009] According to one aspect of the invention there is provided aregenerative adsorption process for application in an adsorptionassembly comprising a condenser, an evaporator and a plurality ofreactors each alternately operating in adsorption and desorption modes,said process comprising:

[0010] passing a coolant through the condenser;

[0011] passing the coolant emanating from the condenser through reactorsoperating in adsorption mode; and

[0012] passing waste heat from a waste heat source through reactorsoperating in desorption mode; wherein said plurality of reactors arescheduled such that each reactor alternately operates in adsorption anddesorption modes for substantially identical time intervals, and suchthat each reactor has an equal chance of being the first reactor toreceive the coolant emanating from the condenser when operating inadsorption mode, and the waste heat from the waste heat source whenoperating in desorption mode.

[0013] According to another aspect of the invention there is provided amulti-reactor regenerative adsorption chiller assembly comprising:

[0014] a condenser adapted to receive a coolant from a source;

[0015] an evaporator connected to said condenser to provide arefrigerant circuit;

[0016] a plurality of reactors, each being able to operate in adsorptionand desorption modes and having a coolant inlet to directly orindirectly receive coolant emitted from said condenser when operating inadsorption mode, and a waste heat inlet for directly or indirectlyreceiving waste heat from a waste heat source when operating indesorption mode; and control means for controlling said plurality ofreactors such that each reactor alternately operates in adsorption anddesorption modes for substantially identical time intervals, and suchthat each reactor has an equal chance of being the first reactor toreceive the coolant emanating from the condenser when operating inadsorption mode, and the waste heat from the waste heat source whenoperating in desorption mode.

[0017] The reactors operating in adsorption mode may be arranged inseries and/or in parallel depending upon the particular operation, andalso depending on the total number of reactors being used. However, thereactors operating in desorption mode are arranged in series.

[0018] In a preferred embodiment, the plurality of reactors comprises aneven number of reactors, wherein at substantially any instant during theprocess, half of the plurality of reactors operate in adsorption modeand the other half of the plurality of reactors operate in desorptionmode. Most preferably, the plurality of reactors comprises at least fourreactors.

[0019] The flow rate of coolant and waste heat through the plurality ofreactors operating in adsorption and desorption modes respectively maybeany suitable flow rate depending on the particular size of chillerassembly and design of heat exchangers. Preferably, the coolant isflowed through the reactors operating in adsorption mode at a suitableflow rate. A suitable flow rate is preferably any flow rate that resultin a transition or turbulent flow regime in the channel of a heatexchanger, be it the chilled water, coolant and/or heat source. When theplurality of reactors comprises four or more reactors, the flow rate ofcoolant through reactors operating in adsorption mode is preferably atthe suitable flow rate, irrespective of whether the reactors operatingin adsorption mode are arranged in series or in parallel. Sizing andflow rates can be determined by those who are skilled in the art.

[0020] The waste heat is preferably flowed through the reactorsoperating in desorption mode at a suitable flow rate. More preferably,where the plurality of reactors comprises four or more reactors, theflow rate of waste heat through reactors operating in desorption mode isalso sized at the suitable flow rate.

[0021] Similarly, the flow rate of coolant through the condenser may bedetermined for a specific application of the invention. It will berecognised that the flow rate of coolant through the reactors operatingin adsorption mode will be somewhat dependent on the flow rate ofcoolant through the condenser. In a preferred embodiment, the flow rateof coolant through the condenser is at a suitable flow rate as describedabove.

[0022] As discussed above, the adsorption assembly comprises acondenser, an evaporator and a plurality of reactors, each of whichalternatively operates in adsorption and desorption modes. In apreferred embodiment, the plurality of reactors are arranged in seriessuch that, in use, reactors operating in adsorption mode constitute afirst sub-series of reactors connected in series and/or in parallel toreceive coolant from the condenser and reactors operating in desorptionmode constitute a second sub-series of reactors connected in series toreceive waste heat from the waste heat source.

[0023] Each reactor is preferably composed of heat exchanging materialand contains adsorbents. The adsorbent could be any material, such assilica gel, that is able to adsorb, either by physisorption and/orchemisorption refrigerant, for example water vapour, ammonia, ormethanol at a typical cooling tower temperature and desorb refrigerantat moderately low temperature (typically 150° C. or below). The coolantfrom a cooling tower is first passed through the condenser andsubsequently to each of the reactors operating in adsorption mode eitherin series or in parallel. The waste heat source is passed serially fromone reactor operating in desorption mode to another reactor in the samemode. After passing through the last reactor operating in desorptionmode, the waste heat is purged from the system.

[0024] The reactors are scheduled such that each reactor alternatelyoperates in adsorption and desorption mode for substantially the sametime interval, and that each reactor has equal chance of being the firstreactor to either receive the coolant emanating from the condenser orthe waste heat. Such a schedule ensures that maximum smoothening ofchilled water outlet temperature is achieved. This arrangement alsofacilitates maximum extraction of energy from the waste heat to maximisecooling capacity. Cooling the condenser first and then the reactorsoperating in adsorption mode ensures that minimum coolant flow rate isused.

BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The accompanying drawing which is incorporated into andconstitutes apart of the description of the invention, illustrates anembodiment of the invention and serves to explain the principles of theinvention. It is to be understood, however, that the drawing is designedfor purposes of illustration only, and not as a definition of the limitsof the invention.

[0026]FIG. 1 is a schematic of one embodiment of an adsorption chillerconstructed according to the present invention showing the operation ofthe multi-reactor regenerative strategy. Fluid flow between reactors hasbeen depicted as top-down. 1 refers to waste heat stream inlet, 2 refersto coolant inlet, 2 a refers to coolant inlet to the reactor, 3 refersto waste heat stream outlet, 4 refers to coolant outlet, and 5 refers tothe outflow of excess coolant. The bold lines depict the refrigerantcircuit, while the thin lines depict the coolant and heat sourcecircuit.

indicates either a manual or elect

[0027]FIG. 2 illustrates the relation of recovery efficiency, η, as afunction of dimensionless cycle time, ω for two-, four-, and six-bedadsorption chillers.

[0028]FIG. 3 illustrates the dimensionless outlet temperature,{overscore (T)} profiles for the chilled water, condenser coolant,adsorber coolant, and waste heat stream for two-, four-, and six-bedadsorption chillers under dynamic-steady-state condition. Due to thechoice of non-dimensionalising the temperature, the chilled water outletdimensionless temperature turns out to be negative, a direct reflectionthat the system is operating as a chiller.

DESCRIPTION OF THE EMBODIMENTS OF THE INVENTION

[0029] In detail now and referring to the drawings, FIG. 1 illustratesone embodiment of the multi-reactor regenerative adsorption chillerassembly of the present invention. The N-reactor regenerative adsorptionchiller consists of N reactors, where N is even to achieve optimalchilled water outlet temperature smoothening, a condenser and anevaporator.

[0030] In general, N/2 reactors operate under adsorption mode, while theother N/2 reactors operate under desorption mode at any instant of useof the adsorption chiller. Coolant from a cooling source enters thecondenser at location 2 and travels through the condenser. Subsequently,the coolant enters one or more reactors operating under adsorption modethrough valve(s) 2 a, depending on whether the reactors are arranged inparallel or in series. A rated amount of coolant flows through thereactors operating under adsorption mode, and is eventually purged fromport(s) 4. Excess coolant from the condenser is removed from port 5.

[0031] Heat source is introduced at any one port 1 and flows seriallythrough all the N/2 reactors operating under desorption mode and ispurged from a port 3. The reactors are scheduled such that each reactoralternately operates in adsorption and desorption mode for the samehalf-cycle time interval, and that each reactor has equal chance ofbeing the first reactor to either receive the coolant emanating from thecondenser through port 2 a or the waste heat through valve 1. The energyschedules may be best understood by referring to the following tables:TABLE 1 The following table illustrates the general schedule for aseries-cooled 4-reactor system. Energy utilization schedule for a4-reactor chiller Reactor sw ads (2) ads (1) sw des (2) des (1) 1Reactor des (1) sw ads (2) ads (1) sw des (2) 2 Reactor sw des (2) des(1) sw ads (2) ads (1) 3 Reactor ads (1) sw des (2) des (1) sw ads (2) 4

[0032] The responding schedule for a parallel-cooled, 4-reactor systemcan be inferred from the table. TABLE 2 The following table illustratesthe general schedule for a series- or and parallel-cooled 6- reactorsystem. Two possible energy utilization schedules for a six-reactorchiller Reactor sw ads(3) ads(2) ads(1) sw des(3) des(2) des(1) 1Reactor des(1) sw ads(3) ads(2) ads(1) sw des(3) des(2) 2 Reactor des(2)des(1) sw ads(3) ads(2) ads(1) sw des(3) 3 Reactor sw des(3) des(2)des(1) sw ads(3) ads(2) ads(1) 4 Reactor ads(1) sw des(3) des(2) des(1)sw ads(3) ads(2) 5 Reactor ads(2) ads(1) sw des(3) des(2) des(1) swads(3) 6

[0033] As discussed above, parallel cooling of one or more of thereactors operating under adsorption mode may be possible. This willgenerally depend on the coolant flow rate through the condenser.Typically, parallel cooling of one or more of the reactors operatingunder adsorption mode is more practical for a system with six or morereactors. TABLE 3 Bed 1 sw ads (N/2) ads(N/2-1)

sw des (N/2) des(N/2-1)

des(2) des(1) Bed 2 des(1) sw ads

ads(1) sw des (N/2)

des(3) des(2)

Bed N/2 + 1 sw des (N/2) des(N/2-1)

sw ads (N/2) ads(N/2-1)

ads(2) ads(1) Bed N/2 + 2 ads(1) sw des (N/2)

des(1) sw ads (N/2)

ads(3) ads(2)

Bed N-1 ads(N/2-2) ads(N/2-3)

des(N/2-2) des(N/2-3)

sw ads (N/s) ads(N/2-1) Bed N ads(N/2-1) ads(N/2-2)

des(N/2-1) des(N/2-2)

des(1) sw ads (N/2) # if it is a series cooling scheme. # the reactorreceives cooling stream from ads(N/2-1). # J < K ≦ N/2, and so on.

[0034] In general, the schedule for an N-reactor chiller, where N iseven, is shown in Table 1. In principle N could be odd, but this wouldnot lead to optimal temperature smoothening of the outlet chilled water.The N-reactor system is advantageously devised to start-up sequentially.Specifically, during start-up, reactors operating under adsorption modeand reactors operating under desorption mode are preferably activatedone at a time so that a sudden depression of the evaporator temperatureis prevented thus reducing the risk of ice formation in the evaporator.

[0035] The following technical analysis is provided only to demonstratethe efficacy of the invention. This analysis has made use of certainspecific technical specifications so as to quantatively demonstrate theadvantages of the invention. It is emphasised that other similaranalyses based on different technical specifications and even differentformalisms are possible. Hence, the associated specifications of thepresent analysis should not, in any way, be construed as restrictive onthe present invention.

[0036] Specifics of the analysis:

[0037] linear driving force (LDF) kinetic equation, equation (1),

[0038] silicagel-water binary system, equation (2),

[0039] lumped-parameter treatment for the reactors, evaporator andcondenser,

[0040] specifications as delineated in Table 4.

[0041] The performance prediction of the proposed multi-bed regenerativestrategy is based on an extension of the verified design code for thecommercial two-bed chiller [15-16]. The structure of the originalformalism is essentially unchanged, except that the energy balances forthe condenser and evaporator have to be augmented to account forinteraction with more than one bed. Heat and mass balance equations mustsimilarly be augmented; they must also handle the additional bedtransients. The rate of adsorption or desorption is governed by thelinear driving force kinetic equation: $\begin{matrix}{\frac{q}{\tau} = {\frac{15t_{cycle}D_{s0}{\exp \left\lbrack {{- E_{a}}/({RT})} \right\rbrack}}{R_{p}^{2}}\left\lbrack {{q^{*}\left( {P,T} \right)} - q} \right\rbrack}} & (1)\end{matrix}$

[0042] The coefficients of which were determined by Chihara and Suzuki[17] and q* is given by the following empirical isotherm equation [19]which is based on the manufacturer's proprietary data [19]:$\begin{matrix}{q^{*} = {{A\left( T_{sg} \right)}\left\lbrack \frac{P_{sat}\left( T_{ref} \right)}{P_{sat}\left( T_{sg} \right)} \right\rbrack}^{B{(T_{sg})}}} & (2)\end{matrix}$

[0043] The energy balance for bed I, ignoring heat losses, during itsinteraction with the evaporator can be written as $\begin{matrix}{{{\left( {1 + \alpha_{Hex}} \right)\frac{{\overset{\_}{T}}_{{bed},I}}{\tau}} + {q_{{bed},I}\frac{{\overset{\_}{h}}_{ads}}{\tau}}} = {{\frac{q_{{bed},I}}{\tau}\left\{ {{\delta_{I}\left\lbrack {{{\overset{\_}{h}}_{g}\left( T_{evap} \right)} - {{\overset{\_}{h}}_{ads}\left( {P_{evap},T_{{bed},I}} \right)}} \right\rbrack} - {\left( {1 - \delta_{I}} \right){\overset{\_}{\Delta \quad H}}_{ads}}} \right\}} - {{NTU}_{cooling}\omega \quad c_{c,i}{\sum\limits_{i = 1}^{N}\quad {\left( {{\overset{\_}{T}}_{{bed},I} - {\overset{\_}{T}}_{i}} \right).}}}}} & \text{(3a)}\end{matrix}$

[0044] The energy balance for the coolant can be expressed as$\begin{matrix}{{{\alpha_{{bed\_ tube},i}\frac{{\overset{\_}{T}}_{i}}{\tau}} = {\omega \left\lbrack {{{\overset{\_}{h}}_{f}\left( T_{i - 1} \right)} - {{\overset{\_}{h}}_{f}\left( T_{i} \right)} + {{NTU}_{cooling}{c_{c,i}\left( {{\overset{\_}{T}}_{{bed},I} - {\overset{\_}{T}}_{i}} \right)}}} \right\rbrack}}{{{for}\quad i} = {{1\quad {to}\quad {N.\quad {{\overset{\_}{T}}_{i}(0)}}} = {{{\overset{\_}{T}}_{bedi}(0)} = {{0.\quad {{\overset{\_}{T}}_{i}(\tau)}} = {{{\overset{\_}{T}}_{N_{2}}(\tau)}_{cond}}}}}}} & \text{(3b)}\end{matrix}$

[0045] when bed I is being cooled directly by the coolant from thecondenser, and {overscore (T)}₁(τ)={overscore (T)}_(N)(τ)|_(bed, I−1)when it is being cooled by the coolant from bed I−1.q_(bed,I)(0)=q*(P_(evap)(0),T_(bed,I)(0)). It has been assumed that therelation {overscore (h)}_(ads) (P, T)={overscore (h)}_(g)(P,T)−{overscore (ΔH)}_(ads) holds at all time, so that the transientisosteric heat of adsorption is insensitive to the instantaneousadsorbate concentration. The isosteric heat of adsorption has beenobtained from the work of Sakoda and Suzuki [20].

[0046] When the bed J is interacting with the condenser, its energybalance can be written as $\begin{matrix}{{{\left( {1 + \alpha_{Hex}} \right)\frac{{\overset{\_}{T}}_{{bed},J}}{\tau}} + {q_{{bed},I}\frac{{\overset{\_}{h}}_{ads}}{\tau}}} = {{\theta_{J}\frac{q_{{bed},J}}{\tau}{\overset{\_}{\Delta \quad H}}_{ads}} - {{NTU}_{heating}\omega {\overset{\_}{\overset{.}{m}}}_{heating}c_{h,i}{\sum\limits_{i = 1}^{N}\quad {\left( {{\overset{\_}{T}}_{{bed},J} - {\overset{\_}{T}}_{i}} \right).}}}}} & \text{(4a)}\end{matrix}$

[0047] The energy balance for the coolant can be expressed as$\begin{matrix}{{\alpha_{{bed\_ tube},i}\frac{{\overset{\_}{T}}_{i}}{\tau}} = {\omega {{\overset{\_}{\overset{.}{m}}}_{heating}\left\lbrack {{{\overset{\_}{h}}_{f}\left( T_{i - 1} \right)} - {{\overset{\_}{h}}_{f}\left( T_{i} \right)} + {{NTU}_{heating}{c_{c,i}\left( {{\overset{\_}{T}}_{{bed},J} - {\overset{\_}{T}}_{i}} \right)}}} \right\rbrack}}} & \text{(4b)}\end{matrix}$

[0048] for i=1 to N. {overscore (T)}_(i)(0)={overscore (T)}_(bed,J)(0)=1. {overscore (T)}_(i)(τ) when bed J is being heated directly by thewaste heat source, and {overscore (T)}₁(τ)={overscore(T)}_(N)(τ)|_(bed,J−1) when it is being regenerated by the heatingstream from bed J-1. q_(bed,J)(0)=q*(P_(cond)(0), T_(bed,J)(0)). Thecondenser has been assumed, relative to the beds and evaporator, to beretaining negligible amount of refrigeration. However, since thecondenser heat exchanging tube has been designed to be corrugated by themanufacturer, the enhanced surfaces will inevitably retain a thin filmof condensate on the surface. This will ensure that the condenser isalways maintained at the refrigerant saturated vapour pressure.Consequently, if dq_(bed,J)/dt>0, θ_(J)=0.

[0049] During bed switching, the bed pressure changes in tandem with thebed temperature. Hence, in the current formalism, such operation hasbeen assumed to be isosteric (i.e. dq/dτ=0). This phase of operationcould still be described by the above equations, and the pressureprescribed by the isotherm equation.

[0050] The evaporator is, in general, interacting with N/2 beds at anytime, its energy balance can be expressed as $\begin{matrix}{{{\left( {\alpha_{ref} + \alpha_{evap}} \right)\frac{{\overset{\_}{T}}_{evap}}{\tau}} + {{{\overset{\_}{h}}_{f}\left( T_{evap} \right)}\frac{q_{ref}}{\tau}}} = {{{- {{\overset{\_}{h}}_{f}\left( T_{cond} \right)}}{\sum\limits_{J = 1}^{n/2}\quad {\theta_{J}\frac{q_{{bed},J}}{\tau}}}} - {{NTU}_{chilled}\omega {\overset{\_}{\overset{.}{m}}}_{chilled}{\sum\limits_{i = 1}^{N_{1}}\quad \left( {{\overset{\_}{T}}_{evap} - {\overset{\_}{T}}_{i}} \right)}} - {\sum\limits_{I = 1}^{n/2}\quad {\left\lbrack {{\delta_{I}{{\overset{\_}{h}}_{g}\left( T_{evap} \right)}} + {\left( {1 - \delta_{I}} \right){{\overset{\_}{h}}_{g}\left( {P_{{evap},}T_{{bed},I}} \right)}}} \right\rbrack \frac{q_{{bed},I}}{\tau}}}}} & \text{(5a)}\end{matrix}$

[0051] The rate of change of liquid refrigerant mass is given by$\begin{matrix}{\frac{q_{ref}}{\tau} = {- {\sum\limits_{k = 1}^{n}\quad {\theta_{k}{\frac{q_{{bed},k}}{\tau}.}}}}} & \text{(5b)}\end{matrix}$

[0052] If bed k is interacting with the evaporator, θ_(k)=1, and if itis interacting with the condenser, θ_(k)=1 when dq_(bed,k)/dt<0 andθ_(k)=0 when dq_(bed)/dt>0.

[0053] The energy balance for the chilled water can be expressed as$\begin{matrix}{{{\alpha_{{evap\_ tube},i}\frac{{\overset{\_}{T}}_{i}}{\tau}} = {\omega {{\overset{\_}{\overset{.}{m}}}_{chilled}\left\lbrack {{{\overset{\_}{h}}_{f}\left( T_{i - 1} \right)} - {{\overset{\_}{h}}_{f}\left( T_{i} \right)} + {{NTU}_{chilled}{c_{{chilled},i}\left( {{\overset{\_}{T}}_{evap} - {\overset{\_}{T}}_{i}} \right)}}} \right\rbrack}}}\quad \quad {{{{for}\quad i} = {{1\quad {to}\quad {N_{1}.\quad {\overset{\_}{\quad T}}_{i}}(0)} = {{{\overset{\_}{T}}_{evap}(0)} = {{{\overset{\_}{T}}_{1}(\tau)} = \frac{T_{{chilled},i} - T_{c,i}}{T_{h,i} - T_{c,i}}}}}},{{{and}\quad {q_{ref}(0)}} = {q_{ref}^{ini}.}}}} & \text{(5c)}\end{matrix}$

[0054] Finally, the energy balance for the condenser which isinteracting with N/2 beds in general and that of its coolant can berespectively expressed as $\begin{matrix}{{{\alpha_{cond}\frac{{\overset{\_}{T}}_{cond}}{\tau}} = {{- {\sum\limits_{J = 1}^{n/2}\quad {{\theta_{J}\left\lbrack {{{\overset{\_}{h}}_{g}\left( {P_{cond},T_{{bed},J}} \right)} - {{\overset{\_}{h}}_{f}\left( T_{cond} \right)}} \right\rbrack}\frac{q_{{bed},J}}{\tau}}}} - {{NTU}_{cond}\omega {\overset{\_}{\overset{.}{m}}}_{cond}{\sum\limits_{i = 1}^{N_{2}}\quad \left( {{\overset{\_}{T}}_{cond} - {\overset{\_}{T}}_{1}} \right)}}}},{and}} & \text{(6a)} \\{{{\alpha_{{cond\_ tube},i}\frac{{\overset{\_}{T}}_{i}}{\tau}} = {\omega {{\overset{\_}{\overset{.}{m}}}_{cond}\left\lbrack {{{\overset{\_}{h}}_{f}\left( T_{i - 1} \right)} - {{\overset{\_}{h}}_{f}\left( T_{i} \right)} + {{NTU}_{cond}{c_{c,i}\left( {{\overset{\_}{T}}_{cond} - {\overset{\_}{T}}_{i}} \right)}}} \right\rbrack}}}\quad {{{for}\quad i} = {{1\quad {to}\quad {N_{2}.\quad {{\overset{\_}{T}}_{i}(0)}}} = {{{\overset{\_}{T}}_{cond}(0)} = {{{\overset{\_}{T}}_{1}(\tau)} = 0.}}}}} & \text{(6b)}\end{matrix}$

[0055] It is intuitively clear that, during the dynamic-steady-stateoperation of an N-bed chiller, where all the beds are operatingsymmetrically, the optimal phase difference between the beds would be2ω/N and that N has to be an even number. This would ensure that thecondenser and evaporator have minimum temperature fluctuation.

[0056] The above mentioned set of coupled equations is solved by theAdams-Moulton method found in the DWVPAG subroutine of the IMSL Fortranlibrary subroutines. The tolerance has been set to 1IE-8. Once theinitial conditions are prescribed, the chiller is allowed to operatefrom transient to dynamic steady state. On a Pentium 233 MHz, 64 MBpersonal computer, it takes about 110 min to calculate a six-bed chilleroperation.

[0057] The non-dimensional cycle averaged cooling power is defined as$\begin{matrix}{{\overset{\_}{Q}}_{e\quad v\quad a\quad p} = {\omega \quad {\overset{\_}{\overset{.}{m}}}_{c\quad h\quad i\quad l\quad l\quad e\quad d}c_{{c\quad h\quad i\quad l\quad l\quad e\quad d},i}{\int_{0}^{1}{\left( {{\overset{\_}{T}}_{{c\quad h\quad i\quad l\quad l\quad e\quad d},i}\quad - {\overset{\_}{T}}_{{c\quad h\quad i\quad l\quad l\quad e\quad d},o}} \right){\quad \tau}}}}} & (7)\end{matrix}$

[0058] As mentioned earlier, since the invention focuses on theutilization of waste heat before it is ultimately purged to theenvironment, its enthalpy relative to that of the environment can beviewed as being a fixed energy input to a system. Consequently,maximising cooling capacity rather than the conventional coefficient ofperformance may be more pertinent. Thus, the following conversionefficiency is accordingly defined: $\begin{matrix}{\eta = {\frac{{\overset{\_}{\overset{.}{m}}}_{c\quad h\quad i\quad l\quad l\quad e\quad d}c_{{c\quad h\quad i\quad l\quad l\quad e\quad d},i}}{{\overset{\_}{\overset{.}{m}}}_{h\quad e\quad a\quad t\quad i\quad n\quad g}c_{h,i}}{\int_{0}^{1}{\left( {{\overset{\_}{T}}_{{c\quad h\quad i\quad l\quad l\quad e\quad d},i}\quad - {\overset{\_}{T}}_{{c\quad h\quad i\quad l\quad l\quad e\quad d},o}} \right){{\quad \tau}.}}}}} & (8)\end{matrix}$

[0059] The environment temperature has been selected to be T_(c,i).

[0060] Performance Comparison of Two-, Four-, and Six-Bed Chillers

[0061] In order to effect a fair evaluation, the performances of thefour- and six-bed chillers operating at an optimal phase difference arecompared against the result of a commercial two-bed chiller.

[0062] The parameters of the commercial two-bed chiller and those of themulti-bed chillers are collated in table 4. It is emphasised that thetotal mass of adsorbent, refrigerant inventory and heat exchangingmaterial have been held fixed. In this description, there are presentedvarious cases when the adsorbers are cooled by the rated flow rate asdelineated in Table 4. This will ensure that heat exchange is undertakenin the transition flow region, so that pumping power is kept to aminimum. One could always pipe all the coolant into the adsorbers. Theimproved heat exchange will be at the expense of pumping power.

[0063] This comparison is meant solely as an example to demonstrate thevirtues of the present invention. In no way should the specific numbersprovided for the various parameters be construed as restrictive on thepresent invention. TABLE 4 Comparison of two-bed and multi-bed chillersspecifications 6-bed Parallel Parameters 2-bed 4-bed Series coolingcooling Total coolant 2.89 1.37 flowrate (kg/s) Total adsorber 1.52(fresh 0.760 (piped 0.507 (piped 1.01 (piped coolant stream from fromfrom from flowrate (kg/s) cooling tower) condenser) condenser)condenser) {dot over (m)}_(heating) 1.28 0.64 0.427 {dot over(m)}_(chilled) 0.71 {dot over (m)}_(cond) 1.37 U_(cooling) 1602.56U_(heating) 1724.14 U_(chilled) 2557.54 U_(cond) 4115.23 A_(bed) 2.461.23 0.820 A_(evap) 1.91 A_(cond) 3.73 M_(sg) 47.0 23.5 15.7c_(p,Hex)M_(Hex) 77719.4 × 10³  38859.7 × 10³  25906.5 × 10³ c_(p,evap)M_(evap) 4805.7 × 10³   c_(p,cond)M_(cond) 9372.08 × 10³  V_(bed)  1.778 × 10⁻²   8.89 × 10⁻³   5.93 × 10⁻³ V_(evap) 6.916 × 10⁻³V_(cond) 1.349 × 10⁻²

[0064] The cost of construction necessarily goes up with the number ofbeds. But depending on the prevailing economic conditions, theperformance improvement of a multi-bed chiller over a two-bed chillercould outweigh the increase in capital investment. Structure wise, thereshould not be a drastic increase in cost. The expensive leak-proof outershell of the two-bed chiller need not be changed significantly. One onlyneeds to weld partitions and, of course, additional insulated piping ineach of the two beds to create a multi-bed system. The fourlarge-bore-size, vacuum-rated solenoid on-off valves of a two-bed systemare replaced, in general, by 2N similar but smaller valves for an N-bedsystem. It is imperative to mention that, just as in a two-bed chiller,these on-off valves and the associated piping have to be designed suchthat the pressure drop between the bed and the evaporator/condenser isminimised. In general, each additional bed requires five normal dutysolenoid gate valves for flow control.

[0065]FIG. 2 shows the recovery efficiency, ρ of the various multi-bedschemes as a function of dimensionless cycle time, ω. The recoveryefficiency of a two-bed chiller at a standard rated ω of 14.55(corresponding to a cycle time of 450s) is 0.0478. It can be appreciatedthat, from two to four beds, the recovery efficiency is boosted by about70%, whereas from four to six beds, the recovery efficiency is increasedby another 40%. The six-bed-parallel configuration can be observed to bemarginally better than its series counterpart, but one has to pay theprice for added complexities. Specifically, flow metering has to be donecarefully during design and commissioning so that there is sufficientflow from the condenser to the two beds in series and the one bed inparallel. One could anticipate that the recovery efficiency improveswith the number of beds, but this has to be balanced with the cost ofconstruction. It is worth mentioning that all these schemes have beenoperated at optimal switching time, ω_(sw) for maximum peak chilledwater outlet temperature suppression. Since the speed of operationreduces with the number of beds, the optimal switching time tends toincrease correspondingly. ω_(sw) for the two-bed, four-bed, six-bedparallel, and six-bed series are 1.13, 1.29, 1.46, and 1.78respectively.

[0066]FIG. 3 illustrates the dimensionless outlet temperatures for thecoolants, waste heat stream and chilled water during dynamic steadystate. The trend for the 6-bed-parallel configuration has been omittedfor clarity. One observes that the waste heat outlet temperaturegenerally decreases with the number of beds, representing a betterutilization of the waste heat before it is purged. The condenser coolantpeak temperature for the two-bed is significantly slashed, rendering itsuitable for subsequent cooling of the adsorbers. In the case ofmulti-bed chillers, chilled water outlet temperature tends to besmoothened. This may lead to the elimination of downstream coolingdevices for demanding process cooling and dehumidification. With thesame amount of resource commitment, chilled water outlet temperature andcycle average cooling capacity necessarily drop but at a rate slowerthan the reduction in heat source and coolant flowrate, resulting in animproved recovery efficiency. In fact heat rejection and input at thevarious components drop with an increase in the number of beds. Coupledwith the fact that there is a better match in temperature between thebed and the coolant/waste heat stream and that the rate of change oftemperature in the beds are slower, the entire chiller is working morereversibly. This result in a mitigation of the various irreversibilitiesidentified and quantified in previous references [16].

[0067] The proposed multi-bed configuration also advantageously reducesthe risk of ice formation in the evaporation upon the initial pull-down.It is customary to purge the beds of any non-condensibles before theinception. In a two-bed chiller, this leads to a vigorous boiling in theevaporator and a sudden temperature depression, increasing the risk ofice formation. Whereas in a multi-bed scheme, the N/2 adsorbers anddesorbers start one at a time. Such a soft-start ensures that theevaporator approaches the targeted temperature in a gradual manner. Thisfurther implies that the total refrigerant inventory in the system canbe reduced.

[0068] The present invention advantageously makes it possible to improvethe recovery efficiency of low grade waste heat via a multi-bedregenerative scheme. This ensures that the enthalpy of waste streamrelative to the environment is better utilized before being purgedeventually. The same scheme can also suppress the chilled water outlettemperature fluctuation. This suggests that downstream temperaturesmoothening device may be downsized or eliminated for those applicationsinvolving demanding process cooling or dehumidification. It is alsoadvantageously able to reduce the oscillation in the condenser coolantoutlet temperature, making it possible to pipe the condenser coolant tofurther cool the adsorbers before finally returning to the coolingtower. For the same cooling capacity, the waste heat and coolantflowrates are reduced, resulting in an economy of piping material. By abetter match between beds and streams temperatures, it has alsoadvantageously been possible to mitigate the heat transfer bottleneckidentified and quantified in previous references [16]. The reduction inthe speed of chiller also reduces the rate of entropy generation.

[0069] It has further been quantified that, compared with a two-bedscheme, a four-bed scheme improves the recovery efficiency by about 70%.Whereas from a four- to a six-bed scheme, the margin of improvement isabout 40%. With a reduction in chiller's speed, optimal switching timealso tends to increase with the number of beds so as to achieve maximumpeak chilled water temperature suppression. Finally, a multi-bed schememakes it possible to start the beds one at a time. This prevents asudden temperature drop in the evaporator, reducing the risk of iceformation. TABLE 5 Cyclic-steady-state dimensionless outlet temperatureprofiles for two-, four-, and six-bed chillers 0 6 62 2700 6 85.074280.61085 34.91316 38.02287 10.63948 33.02395 38.02287 80.61085 0.1254140.896936 −0.370662 0.034854 0.002222 7 1 2701 6.002222 85.10871 80.6346734.95692 38.00587 10.64399 33.00034 85.10871 34.95692 0.978419 0.069872−0.37058 0.034426 0.004444 7 2 2702 6.004444 85.12186 80.65738 35.0132637.98815 10.65137 32.97133 85.12186 35.01326 0.978657 0.070892 −0.3704460.033901 0.006667 7 3 2703 6.006667 84.91622 80.68008 35.12224 37.9630210.66104 32.9433 84.91622 35.12224 0.974931 0.072867 −0.370271 0.0333930.008889 7 4 2704 6.008889 82.7542 80.71429 35.68107 37.86722 10.6725232.91687 82.7542 35.68107 0.935764 0.08299 −0.370063 0.032914 0.011111 75 2705 6.011111 76.27895 80.798 38.09131 37.60416 10.68539 32.892376.27895 38.09131 0.818459 0.126654 −0.36983 0.032469 0.022222 7 6 27106.022222 56.84923 81.39016 58.54128 36.73256 10.75873 32.79927 56.8492358.54128 0.466472 0.497125 −0.368501 0.030784 0.033333 7 7 2715 6.03333354.2324 81.5192 61.4383 36.57665 10.82822 32.73744 54.2324 61.43830.419065 0.549607 −0.367242 0.029664 0.044444 7 8 2720 6.044444 52.2382581.63665 63.60561 36.46012 10.88829 32.68497 52.23825 63.60561 0.3829390.58887 −0.366154 0.028713 0.055556 7 9 2725 6.055556 50.47681 81.7531965.51993 36.36281 10.94148 32.63601 50.47681 65.51993 0.351029 0.623549−0.36519 10.027826 0.066667 7 10 2730 6.066667 48.90493 81.8687867.24673 36.27588 10.98993 32.58932 48.90493 67.24673 0.322553 0.654832−0.364313 0.02698 0.077778 7 11 2735 6.077778 47.49868 81.9832 68.8057936.1955 11.03505 32.54444 47.49868 68.80579 0.297077 0.683076 −0.3634950.026167 0.088889 7 12 2740 6.088889 46.23895 82.09624 70.21434 36.1195611.07771 32.5011 46.23895 70.21434 0.274256 0.708593 −0.362723 0.0253820.093333 7 13 2742 6.093333 45.74963 82.14103 70.73914 36.09043 11.103232.48415 45.74963 70.73914 0.265392 0.7181 −0.362261 0.025075 0.097778 714 2744 6.097778 45.26072 82.18557 71.24326 36.06293 11.13486 32.467445.26072 71.24326 0.256535 0.727233 −0.361687 0.024772 0.102222 7 152746 6.102222 44.80102 82.22985 71.72758 36.03694 11.16192 32.4508544.80102 71.72758 0.248207 0.736007 −0.361197 0.024472 0.106667 7 162748 6.106667 44.39201 82.27385 72.19292 36.01142 11.17914 32.4344844.39201 72.19292 0.240797 0.744437 −0.360885 0.024175 0.111111 7 172750 6.111111 44.03634 82.31764 72.63973 35.98506 11.18448 32.4217244.03634 72.63973 0.234354 0.752531 −0.360788 0.023944 0.115556 7 182752 6.115556 43.72504 82.36585 73.05415 35.95699 11.17843 32.4680343.72504 73.05415 0.228715 0.760039 −0.360898 0.024783 0.12 7 19 27546.12 43.4491 82.42748 73.41611 35.92747 11.16306 32.56832 43.449173.41611 0.223716 0.766596 −0.361176 0.0266 0.124444 7 20 2756 6.12444443.20138 82.50546 73.7208 35.90635 11.14073 32.69564 43.20138 73.72080.219228 0.772116 −0.361581 0.028907 0.128889 7 21 2758 6.12888942.97646 82.59728 73.97658 35.91141 11.1135 32.83169 42.97646 73.976580.215153 0.77675 −0.362074 0.031371 0.133333 7 22 2760 6.133333 42.7718982.69706 74.19966 35.94124 11.08299 32.96486 42.77189 74.19966 0.2114470.780791 −0.362627 0.033784 0.177778 7 23 2780 6.177778 41.6774683.54111 75.84822 36.26883 10.76971 33.77629 41.67746 75.84822 0.1916210.810656 −0.368302 0.048483 0.222222 7 24 2800 6.222222 40.9729684.01023 76.89669 36.23703 10.58274 33.9854 40.97296 76.89669 0.1788580.82965 −0.371689 0.052272 0.266667 7 25 2820 6.266667 40.3516 84.2991977.66962 36.05828 10.50025 33.94428 40.3516 77.66962 0.167601 0.843653−0.373184 0.051527 0.311111 7 26 2840 6.311111 39.79843 84.5055478.32023 35.83459 10.47795 33.8029 39.79843 78.32023 0.15758 0.855439−0.373588 0.048966 0.355556 7 27 2860 6.355556 39.3061 84.67041 78.9106935.60375 10.49031 33.62437 39.3061 78.91069 0.148661 0.866136 −0.3733640.045731 0.4 7 28 2880 6.4 38.86565 84.81153 79.46536 35.37899 10.5233733.43536 38.86565 79.46536 0.140682 0.876184 −0.372765 0.042307 0.4444447 29 2900 6.444444 38.46852 84.93683 79.99309 35.16446 10.5691 33.2473538.46852 79.99309 0.133488 0.885744 −0.371937 0.038901 0.488889 7 302920 6.488889 38.10737 85.05023 80.49646 34.96099 10.62262 33.0654338.10737 80.49646 0.126945 0.894863 −0.370967 0.035606 0.5 7 31 2925 6.538.02201 85.07699 80.61854 34.91185 10.63683 33.02123 38.02201 80.618540.125399 0.897075 −0.37071 0.034805 0.502222 7 32 2926 6.502222 38.0050285.11141 80.64234 34.95565 10.64134 32.99766 85.11141 34.95565 0.9784680.069849 −0.370628 0.034378 0.504444 7 33 2927 6.504444 37.9872985.12446 80.66503 35.01203 10.64873 32.9687 85.12446 35.01203 0.9787040.07087 −0.370494 0.033853 0.506667 7 34 2928 6.506667 37.96216 84.918780.68772 35.12105 10.65841 32.94072 84.9187 35.12105 0.974976 0.072845−0.370319 0.033346 0.508889 7 35 2929 6.508889 37.8663 82.75652 80.7218935.68002 10.66991 32.91433 82.75652 35.68002 0.935807 0.082971 −0.370110.032868 0.511111 7 36 2930 6.511111 37.60306 76.28105 80.80544 38.090810.68279 32.8898 76.28105 38.0908 0.818497 0.126645 −0.369877 0.0324240.522222 7 37 2935 6.522222 36.73099 56.85063 81.39644 58.54516 10.7562232.7969 56.85063 58.54516 0.466497 0.497195 −0.368547 0.030741 0.5333337 38 2940 6.533333 36.57514 54.23315 81.52537 61.44215 10.82579 32.7351354.23315 61.44215 0.419079 0.549677 −0.367286 0.029622 0.544444 7 392945 6.544444 36.45864 52.23877 81.64274 63.60961 10.88594 32.6827152.23877 63.60961 0.382949 0.588942 −0.366197 0.028672 0.555556 7 402950 6.555556 36.36135 50.47712 81.75918 65.52416 10.93919 32.6337950.47712 65.52416 0.351035 0.623626 −0.365232 0.027786 0.566667 7 412955 6.566667 36.27444 48.90502 81.87469 67.25115 10.98772 32.5871548.90502 67.25115 0.322555 0.654912 −0.364353 0.026941 0.577778 7 422960 6.577778 36.19409 47.4986 81.98902 68.81035 11.0329 32.5423247.4986 68.81035 0.297076 0.683159 −0.363534 0.026129 0.588889 7 43 29656.588889 36.11818 46.23873 82.10196 70.21903 11.07562 32.49902 46.2387370.21903 0.274252 0.708678 −0.362761 0.025345 0.593333 7 44 29676.593333 36.08906 45.74941 82.14672 70.74387 11.10111 32.48208 45.7494170.74387 0.265388 0.718186 −0.362299 0.025038 0.597778 7 45 29696.597778 36.06158 45.26056 82.19122 71.24803 11.13275 32.46535 45.2605671.24803 0.256532 0.727319 −0.361726 0.024735 0.602222 7 46 29716.602222 36.03559 44.80095 82.23545 71.73238 11.15978 32.44882 44.8009571.73238 0.248206 0.736094 −0.361236 0.024435 0.606667 7 47 29736.606667 36.01006 44.39201 82.27942 72.19776 11.17698 32.43247 44.3920172.19776 0.240797 0.744525 −0.360924 0.024139 0.611111 7 48 29756.611111 35.98371 44.03639 82.32318 72.64459 11.1823 32.41971 44.0363972.64459 0.234355 0.752619 −0.360828 0.023908 0.615556 7 49 29776.615556 35.95564 43.72512 82.37134 73.05905 11.17624 32.46601 43.7251273.05905 0.228716 0.760128 −0.360938 0.024747 0.62 7 50 2979 6.6235.92612 43.44919 82.43292 73.42105 11.16087 32.56631 43.44919 73.421050.223717 0.766686 −0.361216 0.026563 0.624444 7 51 2981 6.624444 35.90543.20146 82.51085 73.72578 11.13853 32.69363 43.20146 73.72578 0.2192290.772206 −0.361621 0.02887 0.628889 7 52 2983 6.628889 35.91004 42.9765482.60262 73.98159 11.11131 32.82969 42.97654 73.98159 0.215155 0.77684−0.362114 0.031335 0.633333 7 53 2985 6.633333 35.93987 42.7719682.70235 74.20469 11.08081 32.96288 42.77196 74.20469 0.211448 0.780882−0.362666 0.033748 0.677778 7 54 3005 6.677778 36.26754 41.6773 83.5459375.85331 10.76767 33.77446 41.6773 75.85331 0.191618 0.810748 −0.3683390.04845 0.722222 7 55 3025 6.722222 36.23582 40.97268 84.01459 76.9017510.58082 33.98364 40.97268 76.90175 0.178853 0.829742 −0.371724 0.052240.766667 7 56 3045 6.766667 36.05711 40.35121 84.30311 77.67459 10.4984433.94258 40.35121 77.67459 0.167594 0.843743 −0.373217 0.051496 0.8111117 57 3065 6.811111 35.83345 39.798 84.50904 78.3251 10.47625 33.8012339.798 78.3251 0.157573 0.855527 −0.373619 0.048935 0.855556 7 58 30856.855556 35.60263 39.30561 84.67353 78.91543 10.48871 33.62275 39.3056178.91543 0.148652 0.866222 −0.373393 0.045702 0.9 7 59 3105 6.9 35.3779138.86513 84.8143 79.46996 10.52186 33.43379 38.86513 79.46996 0.1406730.876267 −0.372792 0.042279 0.944444 7 60 3125 6.944444 35.1634 38.4679584.9393 79.99753 10.56767 33.24582 38.46795 79.99753 0.133477 0.885825−0.371963 0.038874 0.988889 7 61 3145 6.988889 34.95998 38.1068385.05242 80.50072 10.62126 33.06397 38.10683 80.50072 0.126935 0.894941−0.370992 0.035579 1 7 62 3150 7 34.91084 38.02145 85.07912 80.6227610.63549 33.01978 38.02145 80.62276 0.125389 0.897151 −0.370734 0.0347791.002222 8 1 3151 7.002222 34.95466 38.00446 85.11347 80.64655 10.6400132.99624 85.11347 34.95466 0.978505 0.069831 −0.370652 0.034352 1.0044448 2 3152 7.004444 35.01105 37.98673 85.12644 80.66924 10.6474 32.9673185.12644 35.01105 0.97874 0.070852 −0.370518 0.033828 1.006667 8 3 31537.006667 35.12009 37.9616 84.92059 80.69192 10.65709 32.93936 84.9205935.12009 0.975011 0.072828 −0.370343 0.033322 1.008889 8 4 3154 7.00888935.67914 37.86572 82.7583 80.72606 10.66859 32.913 82.7583 35.679140.935839 0.082955 −0.370134 0.032844 1.011111 8 5 3155 7.011111 38.090237.60243 76.28266 80.8095 10.68148 32.8885 76.28266 38.0902 0.8185260.126634 −0.369901 0.0324 1.022222 8 6 3160 7.022222 58.54696 36.7302456.85174 81.39963 10.75495 32.79568 56.85174 58.54696 0.466517 0.497228−0.36857 0.030719 1.033333 8 7 3165 7.033333 61.44387 36.57443 54.2340281.5285 10.82455 32.73395 54.23402 61.44387 0.419095 0.549708 −0.3673090.029601 1.044444 8 8 3170 7.044444 63.6114 36.45795 52.23945 81.6458310.88474 32.68156 52.23945 63.6114 0.382961 0.588975 −0.366219 0.0286511.055556 8 9 3175 7.055556 65.52608 36.36067 50.47764 81.76223 10.9380232.63266 50.47764 65.52608 0.351044 0.623661 −0.365253 0.027766 1.0666678 10 3180 7.066667 67.25319 36.27378 48.90542 81.87769 10.98658 32.5860448.90542 67.25319 0.322562 0.654949 −0.364374 0.026921 1.077778 8 113185 7.077778 68.81249 36.19345 47.49889 81.99197 11.03179 32.5412447.49889 68.81249 0.297081 0.683197 −0.363555 0.026109 1.088889 8 123190 7.088889 70.22125 36.11755 46.2389 82.10487 11.07453 32.4979646.2389 70.22125 0.274255 0.708718 −0.36278 0.025325 1.093333 8 13 31927.093333 70.74611 36.08843 45.74958 82.1496 11.10002 32.48104 45.7495870.74611 0.265391 0.718227 −0.362318 0.025019 1.097778 8 14 31947.097778 71.2503 36.06095 45.26079 82.19408 11.13164 32.46431 45.2607971.2503 0.256536 0.72736 −0.361746 0.024716 1.102222 8 15 3196 7.10222271.73467 36.03496 44.80124 82.2383 11.15865 32.44779 44.80124 71.734670.248211 0.736135 −0.361256 0.024416 1.106667 8 16 3198 7.10666772.20007 36.00943 44.39234 82.28225 11.17583 32.43145 44.39234 72.200070.240803 0.744566 −0.360945 0.02412 1.111111 8 17 3200 7.111111 72.6469235.98308 44.03675 82.32598 11.18112 32.41872 44.03675 72.64692 0.2343610.752662 −0.360849 0.02389 1.115556 8 18 3202 7.115556 73.06137 35.9550143.72549 82.37414 11.17505 32.4651 43.72549 73.06137 0.228723 0.76017−0.360959 0.02473 1.12 8 19 3204 7.12 73.42334 35.92548 43.4495682.43571 11.15967 32.56543 43.44956 73.42334 0.223724 0.766727 −0.3612380.026548 1.124444 8 20 3206 7.124444 73.72806 35.90437 43.20183 82.5136411.13734 32.69279 43.20183 73.72806 0.219236 0.772248 −0.361642 0.0288551.128889 8 21 3208 7.128889 73.98386 35.90945 42.9769 82.60539 11.1101132.82887 42.9769 73.98386 0.215161 0.776881 −0.362136 0.03132 1.133333 822 3210 7.133333 74.20695 35.9393 42.77232 82.70511 11.07962 32.9620742.77232 74.20695 0.211455 0.780923 −0.362688 0.033733 1.177778 8 233230 7.177778 75.85558 36.26703 41.67756 83.54845 10.76653 33.773741.67756 75.85558 0.191623 0.810789 −0.36836 0.048437 1.222222 8 24 32507.222222 76.90399 36.23533 40.97283 84.01685 10.57976 33.9829 40.9728376.90399 0.178856 0.829782 −0.371743 0.052226 1.266667 8 25 32707.266667 77.67679 36.05663 40.35131 84.30513 10.49744 33.9418 40.3513177.67679 0.167596 0.843782 −0.373235 0.051483 1.311111 8 26 32907.311111 78.32725 35.83299 39.79801 84.51084 10.47531 33.80052 39.7980178.32725 0.157573 0.855566 −0.373636 0.048922 1.355556 8 27 33107.355556 78.91752 35.60219 39.30557 84.67514 10.48782 33.62205 39.3055778.91752 0.148652 0.866259 −0.373409 0.045689 1.4 8 28 3330 7.4 79.4719835.37748 38.86508 84.81572 10.52102 33.43311 38.86508 79.47198 0.1406720.876304 −0.372808 0.042266 1.444444 8 29 3350 7.444444 79.9994835.16299 38.46789 84.94056 10.56688 33.24516 38.46789 79.99948 0.1334760.88586 −0.371977 0.038862 1.488889 8 30 3370 7.488889 80.5026 34.9595838.10673 85.05354 10.62052 33.06334 38.10673 80.5026 0.126934 0.894975−0.371005 0.035568 1.5 8 31 3375 7.5 80.62461 34.91044 38.02136 85.080210.63475 33.01915 38.02136 80.62461 0.125387 0.897185 −0.370747 0.0347671.502222 8 32 3376 7.502222 80.64841 34.95427 38.00437 85.11452 10.6392732.99563 85.11452 34.95427 0.978524 0.069824 −0.370665 0.034341 1.5044448 33 3377 7.504444 80.67109 35.01067 37.98664 85.12744 10.64667 32.9667285.12744 35.01067 0.978758 0.070845 −0.370531 0.033817 1.506667 8 343378 7.506667 80.69377 35.11971 37.96151 84.92155 10.65636 32.9387884.92155 35.11971 0.975028 0.072821 −0.370356 0.033311 1.508889 8 353379 7.508889 80.7279 35.67879 37.86562 82.75921 10.66786 32.9124482.75921 35.67879 0.935855 0.082949 −0.370147 0.032834 1.511111 8 363380 7.511111 80.81128 38.08999 37.6023 76.28351 10.68076 32.8879576.28351 38.08999 0.818542 0.12663 −0.369914 0.03239 1.522222 8 37 33857.522222 81.40097 58.5478 36.73005 56.85242 10.75424 32.79517 56.8524258.5478 0.466529 0.497243 −0.368583 0.03071 1.533333 8 38 3390 7.53333381.52981 61.44464 36.57426 54.23456 10.82387 32.73346 54.23456 61.444640.419104 0.549722 −0.367321 0.029592 1.544444 8 39 3395 7.54444481.64712 63.61219 36.45778 52.23992 10.88407 32.68108 52.23992 63.612190.38297 0.588989 −0.366231 0.028643 1.555556 8 40 3400 7.555556 81.763565.52693 36.3605 50.47804 10.93737 32.63219 50.47804 65.52693 0.3510510.623676 −0.365265 0.027757 1.566667 8 41 3405 7.566667 81.8789467.25408 36.27362 48.90574 10.98594 32.58558 48.90574 67.25408 0.3225680.654965 −0.364385 0.026913 1.577778 8 42 3410 7.577778 81.9932168.81341 36.19328 47.49917 11.03117 32.54078 47.49917 68.81341 0.2970860.683214 −0.363566 0.026101 1.588889 8 43 3415 7.588889 82.10608 70.222236.11739 46.23913 11.07393 32.49752 46.23913 70.2222 0.27426 0.708735−0.362791 0.025317 1.593333 8 44 3417 7.593333 82.15081 70.7470736.08827 45.74981 11.09942 32.4806 45.74981 70.74707 0.265395 0.718244−0.362329 0.025011 1.597778 8 45 3419 7.597778 82.19528 71.2512736.06079 45.26102 11.13103 32.46388 45.26102 71.25127 0.25654 0.727378−0.361757 0.024708 1.602222 8 46 3421 7.602222 82.23949 71.73565 36.034844.80149 11.15804 32.44736 44.80149 71.73565 0.248215 0.736153 −0.3612670.024409 1.606667 8 47 3423 7.606667 82.28343 72.20106 36.00927 44.3926111.1752 32.43102 44.39261 72.20106 0.240808 0.744584 −0.360956 0.0241131.611111 8 48 3425 7.611111 82.32716 72.64792 35.98292 44.03704 11.180532.41829 44.03704 72.64792 0.234367 0.75268 −0.360861 0.023882 1.6155568 49 3427 7.615556 82.3753 73.06238 35.95484 43.72578 11.17442 32.4646543.72578 73.06238 0.228728 0.760188 −0.360971 0.024722 1.62 8 50 34297.62 82.43687 73.42437 35.92533 43.44985 11.15904 32.56498 43.4498573.42437 0.223729 0.766746 −0.361249 0.02654 1.624444 8 51 3431 7.62444482.51478 73.72909 35.90421 43.20212 11.13671 32.69235 43.20212 73.729090.219241 0.772266 −0.361654 0.028847 1.628889 8 52 3433 7.62888982.60653 73.98489 35.90928 42.97718 11.10948 32.82843 42.97718 73.984890.215166 0.7769 −0.362147 0.031312 1.633333 8 53 3435 7.633333 82.7062374.208 35.93912 42.77258 11.07899 32.96163 42.77258 74.208 0.211460.780942 −0.362699 0.033725 1.677778 8 54 3455 7.677778 83.5494775.85666 36.26685 41.67774 10.76594 33.7733 41.67774 75.85666 0.1916260.810809 −0.368371 0.048429 1.722222 8 55 3475 7.722222 84.0177876.90507 36.23516 40.97294 10.5792 33.98252 40.97294 76.90507 0.1788580.829802 −0.371754 0.05222 1.766667 8 56 3495 7.766667 84.30596 77.6778636.05647 40.35138 10.49691 33.94148 40.35138 77.67786 0.167597 0.843802−0.373244 0.051476 1.811111 8 57 3515 7.811111 84.51158 78.3282935.83283 39.79807 10.4748 33.80016 39.79807 78.32829 0.157574 0.855585−0.373645 0.048916 1.855556 8 58 3535 7.855556 84.6758 78.91854 35.6020339.3056 10.48735 33.6217 39.3056 78.91854 0.148652 0.866278 −0.3734180.045683 1.9 8 59 3555 7.9 84.81631 79.47297 35.37732 38.86508 10.5205733.43277 38.86508 79.47297 0.140672 0.876322 −0.372816 0.04226 1.9444448 60 3575 7.944444 84.94109 80.00044 35.16283 38.46789 10.56645 33.2448338.46789 80.00044 0.133476 0.885878 −0.371985 0.038856 1.988889 8 613595 7.988889 85.054 80.50352 34.95942 38.10671 10.62011 33.0630238.10671 80.50352 0.126933 0.894991 −0.371013 0.035562 2 8 62 3600 885.08066 80.62553 34.91029 38.02134 10.63435 33.01884 38.02134 80.625530.125387 0.897202 −0.370755 0.034762

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NOMENELATUCE

[0090] A coefficient appearing in the empirical isotherm correlation

[0091] A_(bed) bed heat transfer area (m²)

[0092] A_(evap) evaporator heat transfer area (m²)

[0093] A_(cond) condenser heat transfer area (m²)

[0094] B index appearing in the empirical isotherm correlation

[0095] c_(p,evap) specific heat capacity of evaporator heat exchangingmaterial (Jkg⁻¹K⁻¹)

[0096] c_(p,cond) specific heat capacity of condenser heat exchangingmaterial (Jkg⁻¹K⁻¹)

[0097] c_(p,Hex) specific heat capacity of heat exchanger tube and fin(Jkg⁻¹H⁻¹)

[0098] c_(p,ref) specific heat capacity of liquid refrigerant (Jkg⁻¹K⁻¹)

[0099] c_(p,sg) specific heat capacity of dry adsorbent (Jkg⁻¹K⁻¹)

[0100] c_(x,i) $\frac{c_{p}\left( T_{x,i} \right)}{c_{p,{s\quad g}}}$

[0101] q fraction of refrigerant adsorbed by the adsorbent (kg per kg ofdry adsorbent)

[0102] q* fraction of refrigerant which can be adsorbed by the adsorbentunder conditions of saturation (kg per kg of dry adsorbent)

[0103] q_(bed,I) fraction of refrigerant adsorbed by the adsorbent inbed I (kg per kg of dry adsorbent)

[0104] q_(ref) ratio of the mass of liquid refrigerant inventory in theevaporator to that of the dry adsorbent (kg per kg of dry adsorbent)

[0105] q_(ref) ^(ini) ratio of the initial mass of liquid refrigerantinventory in the evaporator to that of the dry adsorbent (kg per kg ofdry adsorbent)

[0106] q_(cond) ratio of the mass of condensed refrigerant in thecondenser to that of the dry adsorbent (kg per kg of dry adsorbent)

[0107] E_(a) activation energy of surface diffusion (Jmol⁻¹)

[0108] D_(s0) pre-exponent constant in the kinetics equation (m²s⁻¹)

[0109] h_(ads) specific enthalpy of adsorbate (Jkg⁻¹)

[0110] h_(f) saturated fluid specific enthalpy (Jkg⁻¹)

[0111] {overscore (h)}$\frac{h}{c_{p,{s\quad g}}\left( {T_{h,i} - T_{c,i}} \right)}$

[0112] {dot over (m)}_(chilled) chilled water flowrate (kgs⁻¹)

[0113] {dot over (m)}_(cond) condenser coolant flowrate (kgs⁻¹)

[0114] {dot over (m)}_(cooling) adsorber coolant flowrate (kgs⁻¹)

[0115] {dot over (m)}_(heating) desorber waste heat source flowrate(kgs⁻¹)

[0116] {dot over (m)}$\frac{\overset{.}{m}}{{\overset{.}{m}}_{c\quad o\quad o\quad l\quad i\quad n\quad g}}$

[0117] M_(cond) mass of condenser heat exchanger tube (kg)

[0118] M_(evap) mass of evaporator heat exchanger tube (kg)

[0119] M_(Hex) mass of heat exchanger tube and fin in the bed (kg)

[0120] M_(sg) mass of silica gel mass in one bed (kg)

[0121] n,N₁,N₂ number of discrete elements in the heat exchanging tubes

[0122] NTU_(cooling)$\frac{U_{c\quad o\quad o\quad l\quad i\quad n\quad g}{A_{b\quad e\quad d}/N}}{{\overset{.}{m}}_{c\quad o\quad o\quad l\quad i\quad n\quad g}{c_{p}\left( T_{c,i} \right)}}$$\frac{U_{c\quad h\quad i\quad l\quad l\quad e\quad d}{A_{e\quad v\quad a\quad p}/N_{1}}}{{\overset{.}{m}}_{c\quad h\quad i\quad l\quad l\quad e\quad d}{c_{p}\left( T_{{c\quad h\quad i\quad l\quad l\quad e\quad d},i} \right)}}$$\frac{U_{c\quad o\quad n\quad d}{A_{c\quad o\quad n\quad d}/N_{2}}}{{\overset{.}{m}}_{c\quad o\quad n\quad d}{c_{p}\left( T_{c,i} \right)}}$

[0123] NTU_(chilled)

[0124] NYU_(cond)

[0125] NTU_(heating)$\frac{U_{h\quad e\quad a\quad t\quad i\quad n\quad g}{A_{b\quad e\quad d}/N}}{{\overset{.}{m}}_{h\quad e\quad a\quad t\quad i\quad n\quad g}{c_{p}\left( T_{h,i} \right)}}$

[0126] p pressure (pa)

[0127] P_(cond) condenser pressure (Pa)

[0128] P_(evap) evaporator pressure (Pa)

[0129] P_(sat) saturated vapour pressure (Pa)

[0130] R universal gas constant (Jmol⁻¹K⁻¹ or Jkg⁻¹K⁻¹)

[0131] P_(p) average radius of silica gel (m)

[0132] t time (s)

[0133] t_(cycle) cycle time (s)

[0134] t_(sw) switching time (s)

[0135] T temperature (K. or ° C.)

[0136] T_(bed,I) bed I temperature (K. or ° C.)

[0137] T_(c,i) coolant water inlet temperature to the condenser (K. or °C.)

[0138] T_(chilled,i) chilled water inlet temperature to the evaporatorK. or ° C.)

[0139] T_(chilled,o) chilled water outlet temperature from theevaporator (K. or ° C.)

[0140] T_(cond) condenser temperature (K. or ° C.)

[0141] T_(evap) evaporator temperature (K. or ° C.)

[0142] T_(h,i) waste heat supply temperature to the chiller (K. or ° C.)

[0143] T_(i) temperature of fluid within a discrete element i in theheat exchanging tube (K. or ° C.)

[0144] T_(ref) refrigerant temperature (K. or ° C.)

[0145] T_(sg) silica gel temperature (K. or ° C.)

[0146] {overscore (T)} $\frac{T - T_{c,i}}{T_{h,i} - T_{c,i}}$

[0147] U_(cooling) adsorber heat transfer coefficient (Wm⁻²K⁻¹)

[0148] U_(beating) desorber heat transfer coefficient (Wm⁻²K⁻¹)

[0149] U_(chilled) evaporator heat transfer coefficient (Wm⁻²K⁻¹)

[0150] U_(cond) condenser heat transfer coefficient (Wm^(2K) ⁻¹)

[0151] V_(x) _(—) _(tube) volume of fluid within the heat exchangingtube of component x, where x could be the bed, evaporator, or condenser(m³)

[0152] β_(cond)$\frac{M_{c\quad o\quad n\quad d}c_{p,{c\quad o\quad n\quad d}}}{M_{s\quad g}c_{p,{s\quad g}}}$$\frac{M_{e\quad v\quad a\quad p}c_{{p,{e\quad v\quad a\quad p}}\quad}}{M_{s\quad g}c_{p,{s\quad g}}}$$\frac{M_{H\quad e\quad x}c_{p,{H\quad e\quad x}}}{M_{s\quad g}c_{p,{s\quad g}}}$$\frac{M_{r\quad e\quad f}c_{p,{r\quad e\quad f}}}{M_{s\quad g}c_{p,{s\quad g}}}$$\frac{{\rho \left( T_{i} \right)}V_{x\_ tube}{{c_{p}\left( T_{i} \right)}/N_{x}}}{M_{s\quad g}c_{p,{s\quad g}}};$

[0153] β_(evap)

[0154] β_(Hex)

[0155] β_(ref)

[0156] β_(x—tube,i)

[0157] if x refers to the bed, N_(x)=N, if x refers to the evaporatorand condenser, N_(x)=N₁ and N_(x)=N₂ respectively

[0158] δ_(I),θ_(I) flags governing the transient operation of bed I

[0159] Δ{overscore (H)}_(ads) isosteric heat of adsorption

[0160] {overscore (ΔH)}_(ads)$\frac{\Delta \quad H_{a\quad d\quad s}}{c_{p,{s\quad g}}\left( {T_{h,i} - T_{c,i}} \right)}$

[0161] η conversion efficiency, ratio of cycle averaged cooling capacityto the enthalpy of waste heat stream relative to the environment

[0162] T τ  t/t_(cycle)$\omega \frac{{\overset{.}{m}}_{cooling}t_{cycle}}{M_{sg}}$$\omega_{sw}\frac{{\overset{.}{m}}_{cooling}t_{sw}}{M_{sg}}$

[0163] ω

[0164] ω_(s ω)

We claim:
 1. A regenerative adsorption process for application in anadsorption assembly comprising a condenser, an evaporator and aplurality of reactors each alternately operating in adsorption anddesorption modes, said process comprising: passing a coolant through thecondenser; passing the coolant through reactors operating in adsorptionmode before, after or simultaneous with the passing of the coolantthrough the condenser; and passing waste heat from a waste heat sourcethrough reactors operating in desorption mode; wherein said plurality ofreactors are scheduled such that each reactor alternately operates inadsorption and desorption modes for substantially identical timeintervals, and such that each reactor has an equal chance of being thefirst reactor to receive the coolant emanating from the condenser whenoperating in adsorption mode, and the waste heat from the waste heatsource when operating in desorption mode.
 2. A process according toclaim 1, further comprising the step of arranging said reactorsoperating in adsorption mode in series and/or in parallel.
 3. A processaccording to claim 1, wherein said plurality of reactors comprises aneven number of reactors, further comprising the step of operating atsubstantially any instant during said process half of said plurality ofreactors in adsorption mode and the other half of said plurality ofreactors in desorption mode.
 4. A process according to claim 3, furthercomprising the step of providing at least four reactors.
 5. A processaccording to claim 4, further comprising the step of providing sixreactors.
 6. A process according to claim 1, further comprising the stepof flowing the coolant through said reactors operating in adsorptionmode at a flow rate which provides a transition or turbulent flow regimein the channel of a heat exchanger.
 7. A process according to claim 1,flrher comprising the step of flowing the waste heat through saidreactors operating in desorption mode at a predetermined flow rate.
 8. Aprocess according to claim 1, flrer comprising the step of flowing thecoolant through said condenser at a predetermined flow rate.
 9. Amulti-reactor regenerative adsorption chiller assembly comprising: acondenser adapted to receive a coolant from a source; an evaporatorconnected to said condenser to provide a refrigerant circuit; aplurality of reactors, each being able to operate in adsorption anddesorption modes and having a coolant inlet to directly or indirectlyreceive coolant when operating in adsorption mode before, after orsimultaneous with the condenser, and a waste heat inlet for directly orindirectly receiving waste heat from a waste heat source when operatingin desorption mode; and control means for controlling said plurality ofreactors such that each reactor alternately operates in adsorption anddesorption modes for substantially identical time intervals, and suchthat each reactor has an equal chance of being the first reactor toreceive the coolant when operating in adsorption mode, and the wasteheat from the waste heat source when operating in desorption mode. 10.An assembly according to claim 9, wherein said plurality of reactors arearranged in series such that, in use, reactors operating in adsorptionmode constitute a first sub-series of reactors connected in seriesand/or in parallel to receive the coolant, and reactors operating indesorption mode constitute a second sub-series of reactors connected inseries to receive waste heat from said waste heat source.
 11. Anassembly according to claim 9, wherein said plurality of reactorscomprises an even number of reactors, and wherein in use atsubstantially any instant half of said plurality of reactors operate inadsorption mode and the other half of said plurality of reactors operatein desorption mode.
 12. An assembly according to claim I 1, wherein saidplurality of reactors comprises at least four reactors.
 13. An assemblyaccording to claim 9, wherein each of said plurality of reactors iscomposed of a heat exchanging material and contain an adsorbent, thatbinds adsorbate byphysi-sorption and/or chemi-sorption.
 14. An assemblyaccording to claim 13, wherein said adsorbent comprises silica gel. 15.An assembly according to claim 9, wherein said plurality ofreactorsindirectly or directly receive coolant emitted from said condenser. 16.An assembly according to claim 10, wherein said plurality of reactorsindirectly or directly receive coolant emitted from said condenser. 17.A process according to claim 1, wherein said step of passing the coolantthrough the reactors operating in adsorption mode further comprises thestep of passing the coolant emanating from the condenser through thereactors operating in adsorption mode.